Author | Cercignani, Carlo. author |
---|---|
Title | The Relativistic Boltzmann Equation: Theory and Applications [electronic resource] / by Carlo Cercignani, Gilberto Medeiros Kremer |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2002 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8165-4 |
Descript | X, 384 p. online resource |
1 Special Relativity -- 1.1 Introduction -- 1.2 Lorentz transformations -- 1.3 Tensors in Minkowski spaces -- 1.4 Relativistic mechanics -- 1.5 Electrodynamics in free space -- 2 Relativistic Boltzmann Equation -- 2.1 Single non-degenerate gas -- 2.2 Single degenerate gas -- 2.3 General equation of transfer -- 2.4 Summational invariants -- 2.5 Macroscopic description -- 2.6 Local Lorentz rest frame -- 2.7 Equilibrium distribution function -- 2.8 Trend to equilibrium. H-theorem -- 2.9 The projector ??? -- 2.10 Equilibrium states -- 3 Fields in Equilibrium -- 3.1 The general case -- 3.2 Non-degenerate gas -- 3.3 Degenerate relativistic Fermi gas -- 3.4 Degenerate relativistic Bose gas -- 4 Thermomechanics of Relativistic Fluids -- 4.1 Introduction -- 4.2 Thermodynamics of perfect fluids -- 4.3 Eckart decomposition -- 4.4 Landau and Lifshitz decomposition -- 4.5 Thermodynamics of a single fluid -- 5 ChapmanโEnskog Method -- 5.1 Introduction -- 5.2 Simplified version -- 5.3 The integrals Il, I2 and I3 -- 5.4 Transport coefficients -- 5.5 Formal version -- 5.6 Appendix -- 6 Method of Moments -- 6.1 Introduction -- 6.2 Grad distribution function -- 6.3 Constitutive equations for Taรry and Paร -- 6.4 Linearized field equations -- 6.5 Five-field theory -- 6.6 Maxwellian particles -- 6.7 Combined method of ChapmanโEnskog and Grad -- 7 Chemically Reacting Gas Mixtures -- 7.1 Introduction -- 7.2 Boltzmann and transfer equations -- 7.3 MaxwellโJรผttner distribution function -- 7.4 Thermodynamics of mixtures -- 7.5 Transport coefficients -- 7.6 Onsager reciprocity relations -- 8 Model Equations -- 8.1 Introduction -- 8.2 The characteristic time -- 8.3 Single non-degenerate gas -- 8.4 Single degenerate gas -- 8.5 Relativistic ionized gases -- 8.6 Appendix -- 9 Wave Phenomena in a Relativistic Gas -- 9.1 Introduction -- 9.2 Propagation of discontinuities -- 9.3 Small oscillations -- 9.4 Shock waves -- 10 Tensor Calculus in General Coordinates -- 10.1 Introduction -- 10.2 Tensor components in general coordinates -- 10.3 Affine connection -- 10.4 Covariant differentiation -- 10.5 Spatial metric tensor -- 10.6 Special relativity in general coordinates -- 11 Riemann Spaces and General Relativity -- 11.1 Introduction -- 11.2 Tensors in Riemannian spaces -- 11.3 Curvature tensor -- 11.4 Physical principles of general relativity -- 11.5 Mechanics in gravitational fields -- 11.6 Electrodynamics in gravitational fields -- 11.7 Perfect fluids -- 11.8 Einsteinโs field equations -- 11.9 Solution for weak fields -- 11.10 Exact solutions of Einsteinโs field equations -- 11.11 RobertsonโWalker metric -- 12 Boltzmann Equation in Gravitational Fields -- 12.1 Introduction -- 12.2 Transformation of volume elements -- 12.3 Boltzmann equation -- 12.4 Transfer equation -- 12.5 Equilibrium states -- 12.6 Boltzmann equation in a spherically symmetric gravitational field -- 12.7 Dynamic pressure in a homogeneous and isotropic universe -- 13 The Vlasov Equation and Related Systems -- 13.1 Introduction -- 13.2 The VlasovโMaxwell system -- 13.3 The VlasovโEinstein system -- 13.4 Steady VlasovโEinstein system in case of spherical symmetry -- 13.5 The threshold of black hole formation -- 13.6 Cosmology with the VlasovโEinstein system -- Physical Constants -- Modified Bessel Function